Resumen de Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric

Zoltán M. Balogh, Francesco Serra Cassano , Matthieu Rickly

• We compare the Hausdorff measures and dimensions with respect to the Euclidean and Heisenberg metrics on the first Heisenberg group. The result is a dimension jump described by two inequalities. The sharpness of our estimates is shown by examples. Moreover a comparison between Euclidean and H-rectifiability is given.